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Proof step 2 from proof abs-node-abs-failed (previous step)

abs-failed(buf0 + buf1), abs-node(buf0, nd) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# buf = NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, # buf2 = nd.alignedsize, (buf + buf2 + validtrailer) + buf1 = buf3 + buf4, is-aligned(# buf1, NODE_HEADER_SIZE), is-encoded(nd, subarray(buf2, 0, node-size-headerless(nd))), is-encoded(nodeheader(node-size-headerless(nd), false), buf), is-garbage-header(buf3) ∨ is-encoded(ndhd, buf3) ∧ # buf4 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE) ⊦

Rule argument

Additional information

Used simplifier rules: abs-node: ⊦ abs-node(buf, nd) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize);%abs-failed: ⊦ abs-failed(buf) ↔ # buf ≥ NODE_HEADER_SIZE ∧ is-aligned(# buf, NODE_HEADER_SIZE) ∧ (∃ buf0, buf1. buf = buf0 + buf1 ∧ # buf0 = NODE_HEADER_SIZE ∧ ( is-garbage-header(buf0) ∨ (∃ ndhd. is-encoded(ndhd, buf0) ∧ # buf1 ≤ align↑(ndhd.size, 2 * NODE_HEADER_SIZE))));%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ is-aligned(n0 * n, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ is-aligned(nd.alignedsize, NODE_HEADER_SIZE); (s)% ⊦ m + m = 2 * m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE + n ≠ 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ # validtrailer = NODE_HEADER_SIZE; (s)%is-encoded-size: ⊦ is-encoded(ndhd, buf) → # buf = NODE_HEADER_SIZE; (forward) from specification encoding-fixed-size-nonempty[encoding-node-header]%m ≠ 0 ⊦ is-aligned(n, m) → (m ≤ n ↔ n ≠ 0); (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ #(buf + buf0) = # buf + # buf0; (s)